The sum of any two odd integers is odd.

False. The sum of two odd integers is always even. Write odd numbers as 2m+1 and 2n+1; adding gives (2m+1)+(2n+1)=2(m+n+1), a multiple of 2, hence even. For example, 7+9=16. This is a basic parity rule: odd ≡ 1 (mod 2), so 1+1 ≡ 0 (mod 2), which is even. Parity shows up in number theory and computer science (e.g., parity bits in error checking). Memory tip: each odd has “one extra.” Two odds bring two “extras,” which pair up to make another complete pair—turning the total even.